A stabilized mass-conserving sharp interface method for multiphase flow problems

In this work, a stabilized conservative level-set method is proposed for sharp-interface modeling of two-phase flows. The level-set regularization (sharpening) equation is reformulated as a pseudo convection–diffusion–reaction (CDR) problem, enabling the application of a Variational Multi-Scale (VMS)–based stabilization strategy. This approach allows the use of smaller diffusion coefficients, which greatly enhances robustness in scenarios involving large interface deformations and reduces the risk of nonphysical interface break-up. To further improve stability, the sharpening equation is solved only in a narrow band surrounding the interface, thereby avoiding one of the main instability sources in conservative level-set methods—the reliance on inadequate representation of far-field normal vectors. The employment of this localized formulation is possible within an enriched finite element framework, which naturally supports zero-thickness sharp-interface representations. Restricting the solution domain for the regularization equation not only improves numerical stability but also substantially reduces computational cost. Benchmark validations – including non-zero strain rate velocity field tests, vortex flows, Zalesak’s disk problem, two and three-dimensional rising bubbles, and oscillating droplet simulations – demonstrate the framework’s excellent mass conservation, accurate pressure jump representation, and reduced parasitic currents compared to the previously developed techniques in this context. Remarkably, the proposed E-FEM/CLS framework achieves these high-fidelity results even on relatively coarse meshes.